"We'll see what happens," Castro said when asked point blank if he'd be interested in becoming a vice presidential pick or running for Texas governor. "There's no grand plan."

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A former Democratic mayor of San Antonio, Castro said that he's "very mindful that when January 20 comes around there are two years left" in President Obama's second term in office.

The Hispanic politician has long been considered a rising star within Democratic political circles since his keynote speech at the 2012 Democratic National Convention. His twin brother, Rep. Joaquín Castro (D-Texas), is also another lawmaker to watch.

"I'm trying to do a great job at HUD," Castro said. "I believe that anything that you do in life ... the No. 1 way of being satisfied personally and also to have a great future — whatever that future is — is to just do a fantastic job with what's in front of you because if you don't do that, you can kiss any of that future goodbye. So I'm just trying to do a good job with what's in front of me."

He stopped short of endorsing Clinton for president. She has yet to declare an official candidacy but is widely expected to run and has a formidable lead in early polling.

"Secretary of State Clinton is obviously an extremely talented person who has made fantastic contributions to our national progress over the last couple of decades," he said. "I’m staying out of those politics in this role but I know that she did a great job as secretary of State and I’m confident that if she is elected president, she would do enormous good for the country as well."

During his prepared policy remarks, Castro touted the administration's recent announcement that it was slashing government fees on federally backed mortgages to make it easier for lower-income Americans to receive home financing.

Some conservatives have raised concerns that such a policy will lead to faulty home loans being given to Americans who can't afford houses, similar to the issue that led to the 2008 financial crisis.

"If anything, the underwriting standards are too strict," Castro said, refuting conservative critics. "We went from one extreme where it was too easy to get a home loan [before the crisis] to another extreme where it was too difficult. ... We want to find a strong middle ground."

He said he was unsure whether the new Congress and the administration would be able to take up housing finance reform. He reiterated his thoughts that housing finance reform would likely include the end of taxpayer-backed mortgage giants Fannie Mae and Freddie Mac.

"Folks along the ideological spectrum and partisan spectrum believe that there is a better way out there [than Fannie and Freddie]," he said. "[We can have] a government backstop but do it in a manner that doesn't leave taxpayers on the hook the way they were a few years ago."